We propose to use ab initio quantum mechanical methods to solve directly for the structural and mechanistic properties of the active sites of several proteins involved in oxidation-reduction processes and in reversible bonding of dioxygen. Particular systems that will be studied include: 1) myoglobin/hemoglobin: Here we will determine geometry and bond energies of O2 (and CO, CN, NO, etc.) and how these quantities and the absorption spectra depend upon local environment and spin states. 2) cytochromes: We will examine the changes in geometries and spectra for the reduced and oxidized states using the ligands common to the various cytochromes. We will also study the reaction mechanism of the mono-oxygenase cytochrome P-450. 3) non-heme iron-sulfur proteins: We will examine the geometries and electronic structure for the 1Fe, 2Fe, and 4Fe active sites of rubredoxin and the ferredoxins. 4) copper-containing proteins: Our emphasis here will be upon models relating to cytochrome-c oxidase and to bonding of O2 onto mono-Cu and di-Cu sites. The theoretical methods to be used have just been developed and include electron-correlation effects and allow evaluation of total energies as a function of geometry for bond-dissociation and reactive processes. These methods have only recently been extended to be capable of tackling the above problems and must still be applied to model systems including the transition metals and nearby ligands.